Matches in DBpedia 2014 for { <http://dbpedia.org/resource/Local_cohomology> ?p ?o. }
Showing items 1 to 34 of
34
with 100 items per page.
- Local_cohomology abstract "In algebraic geometry, local cohomology is an analog of relative cohomology. Alexander Grothendieck introduced it in seminars in 1961 written up by Hartshorne (1967), and in 1961-2, later written up as SGA2 by Grothendieck & Raynaud (2005). In the geometric form of the theory, sections ΓY are considered of a sheaf F of abelian groups, on a topological space X, with support in a closed subset Y. The derived functors of ΓY form local cohomology groupsHYi(X,F)There is a long exact sequence of sheaf cohomology linking the ordinary sheaf cohomology of X and of the open set U = X \Y, with the local cohomology groups.The initial applications were to analogues of the Lefschetz hyperplane theorems. In general such theorems state that homology or cohomology is supported on a hyperplane section of an algebraic variety, except for some 'loss' that can be controlled. These results applied to the algebraic fundamental group and to the Picard group.In commutative algebra for a commutative ring R and its spectrum Spec(R) as X, Y can be replaced by the closed subscheme defined by an ideal I of R. The sheaf F can be replaced by an R-module M, which gives a quasicoherent sheaf on Spec(R). In this setting the depth of a module can be characterised over local rings by the vanishing of local cohomology groups, and there is an analogue, the local duality theorem, of Serre duality, using Ext functors of R-modules and a dualising module.".
- Local_cohomology wikiPageExternalLink books?id=5HgmUQsbe5sC.
- Local_cohomology wikiPageExternalLink S0273-0979-99-00785-5.pdf.
- Local_cohomology wikiPageID "3212091".
- Local_cohomology wikiPageRevisionID "538312293".
- Local_cohomology hasPhotoCollection Local_cohomology.
- Local_cohomology subject Category:Cohomology_theories.
- Local_cohomology subject Category:Commutative_algebra.
- Local_cohomology subject Category:Duality_theories.
- Local_cohomology subject Category:Homological_algebra.
- Local_cohomology subject Category:Sheaf_theory.
- Local_cohomology subject Category:Topological_methods_of_algebraic_geometry.
- Local_cohomology type Ability105616246.
- Local_cohomology type Abstraction100002137.
- Local_cohomology type Cognition100023271.
- Local_cohomology type CohomologyTheories.
- Local_cohomology type DualityTheories.
- Local_cohomology type Explanation105793000.
- Local_cohomology type HigherCognitiveProcess105770664.
- Local_cohomology type Know-how105616786.
- Local_cohomology type Method105660268.
- Local_cohomology type Process105701363.
- Local_cohomology type PsychologicalFeature100023100.
- Local_cohomology type Theory105989479.
- Local_cohomology type Thinking105770926.
- Local_cohomology type TopologicalMethodsOfAlgebraicGeometry.
- Local_cohomology comment "In algebraic geometry, local cohomology is an analog of relative cohomology. Alexander Grothendieck introduced it in seminars in 1961 written up by Hartshorne (1967), and in 1961-2, later written up as SGA2 by Grothendieck & Raynaud (2005). In the geometric form of the theory, sections ΓY are considered of a sheaf F of abelian groups, on a topological space X, with support in a closed subset Y.".
- Local_cohomology label "Local cohomology".
- Local_cohomology sameAs m.08zmyn.
- Local_cohomology sameAs Q6664297.
- Local_cohomology sameAs Q6664297.
- Local_cohomology sameAs Local_cohomology.
- Local_cohomology wasDerivedFrom Local_cohomology?oldid=538312293.
- Local_cohomology isPrimaryTopicOf Local_cohomology.